Ridge covers are used to shingle the ridge of a roof. It has become increasing popular to shingle the roof ridge, such that it has the appearance of a shake shingle roof. The present inventor had devised a ridge cover, described in U. S. Pat. No. 4,434,589, with a varying thickness that when installed, produced the shake shingle effect. The change in thickness was created by taking a single flat piece of asphalt composition and folding multiple tabs until the desired thickness was obtained. As shown in FIG. 5 of the '589 patent, the individual pieces were cut out from a roll of asphalt composition into the desired shapes. The cutting of these irregular shaped pieces produced an excess amount of waste asphalt material, that is both costly and difficult to dispose.
U.S. Patent No. 3,913,294 by the same inventor, discloses a ridge cover with a thickened portion that is formed by folding the middle portion of the cover. The '294 covers have to be packed in corrugated boxes which are bulky and costly. The covers can not be stacked on pallets because adjacent covers are supported by the thickened middle portion, wherein the thin portions tend to bend or bow. Therefore what is needed is a ridge cover of varying thickness that can be efficiently stacked and cut from a roll with minimal waste.